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Dotson's right-footed strike from the top of the 18 in the fifth minute of added time stunned LAFC and drew Minnesota within a point of Bob Bradley's side in the Western Conference table.
After losing its first four games of the season, Minnesota is unbeaten in 10 of its last 11.
Carlos Vela opened the scoring for LAFC in the 40th minute with his team-high fifth goal of the season, but Emanuel Reynoso equalised for Minnesota four minutes into the second half.
It appeared Tristan Blackmon's 77th-minute header would be enough to take the three points for the home side, but Dotson had other ideas.
His drive past goalkeeper Tomas Romero left LAFC disappointed after they had dominated possession and controlled the flow of play throughout.